Related papers: A triality Group of nonassociative algebras with i…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
We study homology and cohomology of triassociative algebras with non-trivial coefficients.
Trialitarian automorphisms are related to automorphisms of order 3 of the Dynkin diagram of type D4. Octic etale algebras with trivial discriminant, containing quartic subalgebras, are classified by Galois cohomology with value in the Weyl…
In this paper, we determine the derivation algebra and automorphism group of the twisted N=2 superconformal algebra. Then we generalize the relative results to the generalized twisted N=2 superconformal algebra in the final section.
We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.
Evolution algebras are non-associative algebras inspired from biological phenomena, with applications to or connections with different mathematical fields. There are two natural ways to define an evolution algebra associated to a given…
The principal observation of the present paper is that an inner isotopy (i.e. a principal isotopy defined by an algebra endomorphism) is a very helpful instrument in constructing and studying interesting classes of nonassociative algebras.…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.
We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…
We determine which simple algebraic groups of type $^3D_4$ over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in…
We extend the results of \cite{EJK} on property (T) to certain groups "coordinatized" by nonassociative algebras.
We study the relations between partial and global group cohomology with values in a commutative unital ring $\mathcal{A}$. In particular, for a unital partial action of a group $G$ on $\mathcal{A}$, such that $\mathcal{A}$ is a direct…
Automorphisms of order $2$ are studied in order to understand generalized symmetric spaces. The groups of type $E_6$ we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as…
We define a trivolution on a complex algebra $A$ as a non-zero conjugate-linear, anti-homomorphism $\tau$ on $A$, which is a generalized inverse of itself, that is, $\tau^3=\tau$. We give several characterizations of trivolutions and show…
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.